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Funding has been cut for Queen Street Mill, Helmshore Mills Textile Museum, Museum of Lancashire, Judges' Lodgings and Fleetwood Museum.
Lancashire County Council has now agreed to keep them open until September to allow talks to continue with groups interested in running them.
Green councillor Nick Wilkinson said it was "great news".
He said: "There is really good potential for the future and different ways of working which could generate income."
Cabinet member for environment, planning and cultural services Marcus Johnstone said: "I am pleased to say that we are in active discussions with bodies interested in taking over all five museums, and we will keep the museums open until the end of September to give those discussions the best possible chance of success.
"It may also present an opportunity for other interested parties to come forward."
The authority has to make savings of Â£65m over the next two years.
A reprieve for five of Lancashire's under-threat museums has been welcomed by a Lancaster councillor.